Speaker excursion protection

ABSTRACT

An audio circuit includes an amplifier, a voltage sensor, a current sensor, and an excursion control circuit. The voltage sensor is coupled to an output of the amplifier. The current sensor is coupled to the output of the amplifier. The excursion control circuit is coupled to the amplifier, the voltage sensor, and the current sensor. The excursion control circuit includes back electro-magnetic force (EMF) measurement, a back-EMF model, and excursion protection. The back-EMF measurement is to measure back electro-magnetic force of a speaker based on voltage measurements received from the voltage sensor and current measurements received from the current sensor. The back-EMF model is updated based on measurements of the back-EMF and is converted to an excursion model. The excursion protection is to limit amplitude of audio signal provided to the amplifier based on the excursion model of the speaker and amplitude of an audio input signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to India Provisional PatentApplication No. 201841046810, filed Dec. 11, 2018, entitled “ExcursionProtection of Passive Radiator and Ported Speakers Using a NovelFeedback Algorithm,” which is hereby incorporated herein by reference inits entirety.

BACKGROUND

To enhance bass response, some loudspeaker systems may include a passiveradiator or a bass reflex port, in addition to a speaker. A passiveradiator is similar to a speaker, but lacks a voice coil and magnet. Ina passive radiator, the mass of the cone, the radiation inertia, and thestiffness of the suspension system form a resonant system whichinteracts with the speaker by coupling through the enclosed air of thespeaker housing. A bass reflex port is an open tube that couples theinterior of a speaker housing to air outside the speaker housing.

SUMMARY

Circuitry to protect a speaker system that includes a passive radiatoror a bass reflex port from damage caused by excessive excursion isdisclosed herein. In one example, an audio circuit includes a speakerhousing, an amplifier, a voltage sensor, a current sensor and anexcursion control circuit. The speaker housing includes a speaker, and apassive radiator or a bass reflex port. The amplifier is coupled to thespeaker. The voltage sensor is coupled to the speaker. The currentsensor is coupled to the speaker. The excursion control circuit iscoupled to the amplifier, the voltage sensor, and the current sensor.The excursion control circuit includes back electro-magnetic force (EMF)measurement, a back-EMF model, and excursion protection. The back-EMFmeasurement is to measure back-EMF of the speaker based on voltagemeasurements received from the voltage sensor and current measurementsreceived from the current sensor. The back-EMF model is updated based onmeasurements of the back-EMF and is converted to an excursion model. Theexcursion protection is to limit amplitude of audio signal provided tothe amplifier based on the excursion model of the speaker and amplitudeof an audio input signal.

In another example, an audio circuit includes an amplifier, a voltagesensor, a current sensor, and an excursion control circuit. The voltagesensor is coupled to an output of the amplifier. The current sensor iscoupled to the output of the amplifier. The excursion control circuit iscoupled to the amplifier, the voltage sensor, and the current sensor.The excursion control circuit includes back-EMF measurement, a back-EMFmodel, and excursion protection. The back-EMF measurement is to measureback electro-magnetic force of a speaker based on voltage measurementsreceived from the voltage sensor and current measurements received fromthe current sensor. The back-EMF model is updated based on measurementsof the back-EMF and is converted to an excursion model. The excursionprotection is to limit amplitude of audio signal provided to theamplifier based on the excursion model of the speaker and amplitude ofan audio input signal.

In a further example, an audio circuit includes an amplifier, a voltagesensor, a current sensor, and an excursion control circuit. The voltagesensor is coupled to an output of the amplifier. The current sensor iscoupled to the output of the amplifier. The excursion control circuitincludes a back-EMF measurement circuit, a second order back-EMF filter;a fourth order back-EMF filter, a port detection circuit, a back-EMFmodel to excursion model conversion circuit, and an excursion protectioncircuit. The back-EMF measurement circuit is coupled to an output of thevoltage sensor and an output of the current sensor. The second orderback-EMF filter is coupled to the back-EMF measurement circuit. Thefourth order back-EMF filter is coupled to the second order back-EMFfilter. The port detection circuit is coupled to the output of thevoltage sensor, the output of the current sensor, and an input of thesecond order filter. The back-EMF model to excursion model conversioncircuit is coupled to an output of the second order back-EMF filter andan output of the fourth order back-EMF filter. The excursion protectioncircuit coupled to an output of the back-EMF model to excursion modelconversion circuit, an audio input, and an input of the amplifier.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed description of various examples, reference will now bemade to the accompanying drawings in which:

FIG. 1 shows a block diagram for an example audio circuit including aspeaker system having a passive radiator;

FIG. 2 show a block diagram for an example audio circuit including aspeaker system having a bass reflex port;

FIG. 3 shows an electrical equivalent circuit for a speaker system thatincludes a passive radiator or a bass reflex port;

FIG. 4 shows an example block diagram for an audio circuit that includesan excursion control circuit in accordance with the present disclosure;

FIG. 5 shows an example block diagram for a port detection circuit inaccordance with the present disclosure; and

FIG. 6 shows an example of operation of an excursion control circuit inaccordance with the present disclosure.

DETAILED DESCRIPTION

Certain terms have been used throughout this description and claims torefer to particular system components. As one skilled in the art willappreciate, different parties may refer to a component by differentnames. This document does not intend to distinguish between componentsthat differ in name but not function. In this disclosure and claims, theterms “including” and “comprising” are used in an open-ended fashion,and thus should be interpreted to mean “including, but not limited to .. . .” Also, the term “couple” or “couples” is intended to mean eitheran indirect or direct wired or wireless connection. Thus, if a firstdevice couples to a second device, that connection may be through adirect connection or through an indirect connection via other devicesand connections. The recitation “based on” is intended to mean “based atleast in part on.” Therefore, if X is based on Y, X may be a function ofY and any number of other factors.

To improve bass response and sound pressure level, speaker systems thatinclude passive radiators or bass reflex ports are sometime driven hardat low frequencies, which may damage the speaker. Various excursionprotection techniques have been applied to reduce such damage. Automaticgain control (AGC) has been applied to limit the peak androot-mean-squared (RMS) power applied to the speaker. However, AGC basedsystems are overly conservative and significantly reduce the lowfrequency output by using high pass filters. High pass filters are usedbecause a speaker's rated power is related to the thermal capacity ofthe speaker, so driving the speaker even at rated power at lowfrequencies will result in over excursion and speaker damage. Modelbased excursion control is also used to reduce speaker damage, andprovides good bass and sound pressure level response at low frequencies.However, model based systems suffer from reliability issues. Forexample, model based systems cannot adapt to variations across speakerlot/temperature/aging, or changes due to opening or closing of the bassreflex port.

The excursion control circuits of the present disclosure include anexcursion model that is updated based on real-time measurements ofspeaker current and voltage. Speaker excursion is estimated by filteringaudio input using the adaptive excursion model. A limiter circuitcompresses the audio signal if the estimated excursion exceeds a safetythreshold. The limiting applies a look-ahead control technique toeliminate over excursion of the speaker. The excursion control circuitsdisclosed herein provide reliable excursion protection while enablingsound pressure levels and bass response that is substantially higherthan other techniques.

FIG. 1 shows a block diagram for an example audio circuit 100 includinga speaker system 102 having a passive radiator 108. The audio circuit100 includes the speaker system 102 and a speaker driver circuit 110.The speaker system 102 includes a speaker 106 and the passive radiator108. The speaker 106 includes a magnet and voice coil, while the passiveradiator 108 lacks a magnet and voice coil. The speaker system 102 iscoupled to the speaker driver circuit 110. The speaker driver circuit110 receives an audio input signal 114 and generates an output signal116 to actuate the speaker 106. The speaker driver circuit 110 includesan excursion control circuit 112 as disclosed herein to limit excursionof the speaker 106 and prevent damage thereto.

FIG. 2 show a block diagram for an example audio circuit 200 including aspeaker system 202 having a bass reflex port 208. The audio circuit 200includes the speaker system 202 and a speaker driver circuit 210. Thespeaker system 202 includes a speaker 206 and the bass reflex port 208.The speaker system 202 is coupled to the speaker driver circuit 210. Thespeaker driver circuit 210 receives an audio input signal 214 andgenerates an output signal 216 to actuate the speaker 206. The speakerdriver circuit 210 includes an excursion control circuit 212 asdisclosed herein to limit excursion of the speaker 206 and preventdamage thereto.

FIG. 3 shows an electrical equivalent circuit 300 for a speaker systemthat includes a passive radiator or a bass reflex port (e.g., thespeaker system 102 or the speaker system 202). In the electricalequivalent circuit 300:

V(t) is input voltage;

I(t) is loop current;

X(t) is excursion;

Bl is force factor;

R_(E) is DC resistance of the voice coil;

R_(MS) is mechanical dampening of the speaker;

C_(MS) is mechanical compliance of the speaker;

M_(MS) is mechanical mass of the speaker;

S_(D) is radiating area of the speaker;

C_(AB) is housing compliance;

R_(AP) is mechanical dampening of the passive radiator;

C_(AP) is mechanical compliance of the passive radiator;

M_(AP) is mechanical mass of the passive radiator or the bass reflexport;

R_(AL) is the mechanical loss of the port.

For a speaker system that includes a passive radiator, R_(AL)→∞. For aspeaker system that includes a bass reflex port, R_(AP)→0 and C_(AP)→∞.The parameters of a speaker vary across lots, with temperature, and withage, while the passive radiator and bass reflex ports parameters do notchange.

The back electro-motive force (EMF) transfer function for a speaker is afourth order system that is expressed as:

$\begin{matrix}{{{{BEMF}(t)} = {{V(t)} - {{I(t)}R_{E}}}}{\frac{{BEMF}(s)}{I(s)} = {{H(s)} = \frac{{B_{3}s^{3}} + {B_{2}s^{2}} + {B_{1}s}}{s^{4} + {A_{3}s^{3}} + {A_{2}s^{2}} + {A_{1}s} + A_{0}}}}} & (1)\end{matrix}$

For a speaker system that includes a passive radiator:

${B_{3} = \frac{B\; l^{2}}{M_{MS}}},{B_{2} = \frac{{Bl}^{2}R_{AP}}{M_{MS}M_{AP}}},{B_{1} = \frac{B\;{l^{2}( {C_{AP} + C_{AB}} )}}{M_{MS}C_{AP}C_{AB}}}$${A_{3} = {\frac{R_{AP}}{M_{AP}} + \frac{R_{MS}}{M_{MS}}}},{A_{2} = {\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} + \frac{R_{AP}R_{MS}}{M_{AP}M_{MS}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$${A_{1} = {{\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} \times \frac{R_{MS}}{M_{MS}}} + {\frac{R_{AP}}{M_{AP}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}},{A_{0} = \frac{C_{AP} + C_{AB} + {s_{d}^{2}C_{MS}}}{M_{MS}C_{MS}M_{AP}C_{AP}C_{AB}}}$

For a speaker system that includes a bass reflex port:

${B_{3} = \frac{B\; l^{2}}{M_{MS}}},{B_{2} = \frac{{Bl}^{2}}{M_{MS}C_{AB}R_{AL}}},{B_{1} = \frac{B\; l^{2}}{M_{MS}M_{AP}C_{AB}}}$${A_{3} = {\frac{1}{C_{AB}R_{AL}} + \frac{R_{MS}}{M_{MS}}}},{A_{2} = {\frac{1}{M_{AP}C_{AB}} + {\frac{1}{C_{AB}R_{AL}} \times \frac{R_{MS}}{M_{MS}}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$${A_{1} = {\frac{R_{MS}}{M_{AP}C_{AB}M_{MS}} + {\frac{1}{C_{AB}R_{AL}} \times \frac{1}{M_{MS}C_{MS}}}}},{A_{0} = \frac{1}{M_{MS}C_{MS}M_{AP}C_{AB}}}$

The speaker excursion transfer function is a fourth order system that isexpressed as:

$\frac{X(s)}{V(s)} = {{\overset{\_}{H}(s)} = \frac{{\overset{\_}{B_{2}}s^{2}} + {\overset{\_}{B_{1}}s} + \overset{\_}{B_{0}}}{s^{4} + {\overset{\_}{A_{3}}s^{3}} + {\overset{\_}{A_{2}}s^{2}} + {\overset{\_}{A_{1}}s^{1}} + \overset{\_}{A_{0}}}}$

For a speaker system that includes a passive radiator:

${\overset{\_}{B_{2}} = \frac{B\; l}{M_{MS}R_{E}}},{\overset{\_}{B_{1}} = \frac{{BlR}_{AP}}{M_{MS}R_{E}M_{AP}}},{\overset{\_}{B_{0}} = \frac{B\;{l( {C_{AP} + C_{AB}} )}}{M_{MS}R_{E}M_{AP}C_{AP}C_{AB}}}$${\overset{\_}{A_{3}} = {\frac{R_{AP}}{M_{AP}} + \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}}},{\overset{\_}{A_{2}} = {\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} + {\frac{R_{AP}}{M_{AP}} \times \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$${\overset{\_}{A_{1}} = {{\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} \times \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{R_{AP}}{M_{AP}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}},{\overset{\_}{A_{0}} = \frac{C_{AP} + C_{AB} + {s_{d}^{2}C_{MS}}}{M_{MS}C_{MS}M_{AP}C_{AP}C_{AB}}}$

For a speaker system that includes a bass reflex port:

${\overset{\_}{B_{2}} = \frac{B\; l}{M_{MS}R_{E}}},{\overset{\_}{B_{1}} = \frac{Bl}{M_{MS}R_{E}C_{AB}R_{AL}}},{\overset{\_}{B_{0}} = \frac{B\; l}{M_{MS}R_{E}M_{AP}C_{AB}}}$${\overset{\_}{A_{3}} = {\frac{1}{C_{AB}R_{AL}} + \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}}},{\overset{\_}{A_{2}} = {\frac{1}{M_{AP}C_{AB}} + {\frac{1}{C_{AB}R_{AL}} \times \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$${\overset{\_}{A_{1}} = {{\frac{1}{M_{AP}C_{AB}} \times \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{1}{C_{AB}R_{AL}} \times \frac{1}{M_{MS}C_{MS}}}}},{\overset{\_}{A_{0}} = \frac{1}{M_{MS}C_{MS}M_{AP}C_{AB}}}$

FIG. 4 shows an example block diagram for an audio circuit 400 thatincludes an excursion control circuit 402 in accordance with the presentdisclosure. The excursion control circuit 402 is an implementation ofthe excursion control circuit 112 or the excursion control circuit 212.The audio circuit 400 includes an amplifier 404 coupled to the excursioncontrol circuit 402, a speaker system 406 that is coupled to theamplifier 404, a current sensor 408, and a voltage sensor 410. Theamplifier 404 is a class-D amplifier in some implementations of theaudio circuit 400. The speaker system 406 is an implementation of thespeaker system 102 or the speaker system 202, and includes a passiveradiator or a bass reflex port. The current sensor 408 and the voltagesensor 410 are coupled to the amplifier 404, the speaker system 406 andthe excursion control circuit 402. The current sensor 408 and thevoltage sensor 410 respectively measure current and voltage in thespeaker system 406. The excursion control circuit 402 applies thecurrent and voltage measurements to update tracking of a back-EMF filterused to estimate excursion of a speaker in the speaker system 406.

The excursion control circuit 402 includes back-EMF measurement 412, aback-EMF model 414, excursion protection 416, port detection 418, andback-EMF model to excursion model conversion 420. The back-EMFmeasurement 412 is coupled to the current sensor 408 and the voltagesensor 410, and determines values of Back-EMF of the speaker system 406per equation (1). The DC resistance R_(E) can be temperature dependent,and can vary over time in some examples of the speaker system 406. Insome implementations of the audio circuit 400, a pilot tone generator436 injects a very low frequency signal into the amplifier 404 via thesummation circuit 438 so that R_(E) can be estimated. By measuring thelow-frequency component of V(t) and I(t) denoted respectively asV_(lf)(t) and I_(lf)(t) the DC resistance R_(E) can be estimated by

$R_{E} = {\frac{V_{lf}(t)}{I_{lf}(t)}.}$Since the pilot tone is at very low frequency (close to DC), themeasurement of R_(E) is very accurate and very close to the DCresistance value. The measured back-EMF values are filtered around aresonant frequency of the speaker in some implementations.

In the back-EMF model 414, the fourth order back-EMF filter H(s) issplit into a second order filter (H₁(s)) 422 and a fourth order filter(H₂(s)) 424.

$\frac{{BEMF}(s)}{I(s)} = {{H(s)} = {{H_{1}(s)} \times {H_{2}(s)}}}$

The second order filter 422 includes only driver elements (i.e., speakerelements), which are variable.

${{H_{1}(s)} = \frac{B_{1}^{\prime}s}{s^{2} + {A_{1}^{\prime}s} + A_{0}^{\prime}}},{B_{1}^{\prime} = \frac{{Bl}^{2}}{M_{MS}}},{A_{1}^{\prime} = \frac{R_{MS}}{M_{MS}}},{A_{0}^{\prime} = {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{S_{d}^{2}}{C_{AB}}} )}}$

The fourth order filter 424 includes both the driver elements and thepassive radiator or bass reflex port elements, which are fixed. Thesecond order filter 422 is coupled to the back-EMF measurement 412, andis continuously adapted to track measured speaker back-EMF provided bythe back-EMF measurement 412 by minimizing the error between theestimated back-EMF generated by the second order filter 422 and themeasured speaker back-EMF provided by the back-EMF measurement 412. Someimplementations of the second order filter 422 employ least-squaresminimization. The fourth order filter 424 is coupled to the second orderfilter 422, and updated based on output of the second order filter 422.H₂(s) has a weak effect on H(s) near resonance of the speaker, andfiltering of the measured back-EMF about speaker resonance in theback-EMF measurement 412 makes error minimization based on H₁(s)effective and accurate.

Back-EMF error minimization in the second order filter 422 is expressedas:BEMF(s)=H ₁(s)H ₂(s)I(s)BEMF_(est)(t)=H ₁(t)⊕H ₂(t)⊕I(t)BEMF_(act)(t)=V(t)−I(t)R _(E)Err(t)=BEMF_(act)(t)−BEMF_(err)(t)

For a speaker system 406 that includes a passive radiator, the fourthorder filter 424 is described as:

${H_{2}(s)} = \frac{s^{4} + {B_{3}^{''}s^{3}} + {B_{2}^{''}s^{2}} + {B_{1}^{''}s} + B_{0}^{''}}{s^{4} + {B_{3}^{''}s^{3}} + {B_{2}^{''}s^{2}} + {B_{1}^{''}s} + A_{0}^{''}}$${B_{3}^{''} = {\frac{R_{AP}}{M_{AP}} + \frac{R_{MS}}{M_{MS}}}},{B_{2}^{''} = {\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} + {\frac{R_{AP}}{M_{AP}} \times \frac{R_{MS}}{M_{MS}}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$$B_{1}^{''} = {{\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} \times \frac{R_{MS}}{M_{MS}}} + {\frac{R_{AP}}{M_{AP}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}$$B_{0}^{''} = {\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}$$A_{0}^{''} = \frac{C_{AP} + C_{AB} + {s_{d}^{2}C_{MS}}}{M_{MS}C_{MS}M_{AP}C_{AP}C_{AB}}$

For a speaker system 406 that includes a bass reflex port, the fourthorder filter 424 is described as:

${H_{2}(s)} = \frac{s^{4} + {B_{3}^{''}s^{3}} + {B_{2}^{''}s^{2}} + {B_{1}^{''}s} + B_{0}^{''}}{s^{4} + {B_{3}^{''}s^{3}} + {B_{2}^{''}s^{2}} + {A_{1}^{''}s} + A_{0}^{''}}$${B_{3}^{''} = {\frac{1}{C_{AB}R_{AL}} + \frac{R_{MS}}{M_{MS}}}},{B_{2}^{''} = {\frac{1}{M_{AP}C_{AP}} + {\frac{1}{R_{AL}C_{AB}} \times \frac{R_{MS}}{M_{MS}}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$$B_{1}^{''} = {{\frac{1}{M_{AP}C_{AB}} \times \frac{R_{MS}}{M_{MS}}} + {\frac{1}{R_{AL}C_{AB}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}$$B_{0}^{''} = {\frac{1}{M_{AP}C_{AB}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}$$A_{1}^{''} = {{\frac{1}{M_{AP}C_{AB}} \times \frac{R_{MS}}{M_{MS}}} + {\frac{1}{R_{AL}C_{AB}} \times \frac{1}{M_{MS}C_{MS}}}}$$A_{0}^{''} = \frac{1}{M_{MS}C_{MS}M_{AP}C_{AB}}$

The excursion protection 416 is coupled to the back-EMF model toexcursion model conversion 420, an audio input 434, and the amplifier404. The excursion model generated by the back-EMF model to excursionmodel conversion 420 is provided to the excursion protection 416. Thespeaker excursion model is also decomposed in second order and fourthorder filters.

$\frac{X(s)}{V(s)} = {{\overset{\_}{H}(s)} = {{\overset{\_}{H_{1}}(s)} \times {\overset{\_}{H_{2}}(s)}}}$${{H_{1}(s)} = \frac{{\overset{\_}{B_{0}}}^{\prime}}{s^{2} + {{\overset{\_}{A_{1}}}^{\prime}s} + {\overset{\_}{A_{0}}}^{\prime}}},{{\overset{\_}{B_{0}}}^{\prime} = \frac{Bl}{M_{MS}R_{E}}},{{\overset{\_}{A_{1}}}^{\prime} = \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}},{{\overset{\_}{A_{0}}}^{\prime} = {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}$

The fourth order excursion filter for a speaker with a passive radiatoris expressed as:

$\mspace{20mu}{{\overset{\_}{H_{2}}(s)} = \frac{s^{4} + {{\overset{\_}{B_{3}}}^{''}s^{3}} + {{\overset{\_}{B_{2}}}^{''}s^{2}} + {{\overset{\_}{B_{1}}}^{''}s} + {\overset{\_}{B_{0}}}^{''}}{s^{4} + {{\overset{\_}{B_{3}}}^{''}s^{3}} + {{\overset{\_}{B_{2}}}^{''}s^{2}} + {{\overset{\_}{B_{1}}}^{''}s} + {\overset{\_}{A_{0}}}^{''}}}$$\mspace{20mu}{{{\overset{\_}{B_{3}}}^{''} = {\frac{R_{AP}}{M_{AP}} + \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}}},{{\overset{\_}{B_{2}}}^{''} = {\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} + {\frac{R_{AP}}{M_{AP}} \times \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}}$$\mspace{20mu}{{\overset{\_}{B_{1}}}^{''} = {{\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} \times \frac{R_{MS}\frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{R_{AP}}{M_{AP}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$$\mspace{20mu}{{\overset{\_}{B_{0}}}^{''} = {\frac{C_{AP} + C_{AB}}{M_{AP}C_{AP}C_{AB}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}$$\mspace{20mu}{{\overset{\_}{A_{0}}}^{''} = \frac{C_{AP} + C_{AB} + {s_{d}^{2}C_{MS}}}{M_{MS}C_{MS}M_{AP}C_{AP}C_{AB}}}$

The fourth order excursion filter for a speaker and bass reflex port isexpressed as:

$\mspace{20mu}{{\overset{\_}{H_{2}}(s)} = \frac{s^{4} + {{\overset{\_}{B_{3}}}^{''}s^{3}} + {{\overset{\_}{B_{2}}}^{''}s^{2}} + {{\overset{\_}{B_{1}}}^{''}s} + {\overset{\_}{B_{0}}}^{''}}{s^{4} + {{\overset{\_}{B_{3}}}^{''}s^{3}} + {{\overset{\_}{B_{2}}}^{''}s^{2}} + {{\overset{\_}{A_{1}}}^{''}s} + {\overset{\_}{A_{0}}}^{''}}}$$\mspace{20mu}{{{\overset{\_}{B_{3}}}^{''} = {\frac{1}{C_{AB}R_{AL}} + \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}}},{{\overset{\_}{B_{2}}}^{''} = {\frac{1}{M_{AP}C_{AB}} + {\frac{1}{R_{AL}C_{AB}} \times \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}}$$\mspace{20mu}{{\overset{\_}{B_{1}}}^{''} = {{\frac{1}{M_{AP}C_{AB}} \times \frac{R_{MS}\frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{1}{R_{AL}C_{AB}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}}$$\mspace{20mu}{{\overset{\_}{B_{0}}}^{''} = {\frac{1}{M_{AP}C_{AB}} \times \frac{1}{M_{MS}}( {\frac{1}{C_{MS}} + \frac{s_{d}^{2}}{C_{AB}}} )}}$$\mspace{20mu}{{\overset{\_}{A_{1}}}^{''} = {{\frac{1}{M_{AP}C_{AB}} \times \frac{R_{MS} + \frac{{Bl}^{2}}{R_{E}}}{M_{MS}}} + {\frac{1}{R_{AL}C_{AB}} \times \frac{1}{M_{MS}C_{MS}}}}}$$\mspace{20mu}{{\overset{\_}{A_{0}}}^{''} = \frac{1}{M_{MS}C_{MS}M_{AP}C_{AB}}}$

In the speaker system 406, H₁(s) and H₂(s) are in the back-EMF domain

$( \frac{{BEMF}(s)}{I(s)} ),$and H₁ (s) and H₂ (s) are in the excursion domain

$( \frac{X(s)}{V(s)} ).$The back-EMF model 414 (including 2^(nd) order filter H₁(s) and 4^(th)order filter H₂(s)) is converted to excursion model (including 2^(nd)order filter H₁ (s) and 4^(th) order filter H₂ (s)) by the back-EMFmodel to excursion model conversion 420. Although these equations arerepresented by the continuous time variable “s”, the actualimplementation uses the discrete time variable “z”. The back-EMF modelto excursion model conversion 420 is coupled to the second order filter422 and the fourth order filter 424. Conversion from back-EMF domain toexcursion domain includes sample rate conversion where H₁(s) and H₂ (s)are computed at a lower sample rate

$( {{e.g.},\;\frac{f_{s}}{N}} ),$and H₁ (s) and H₂ (s) are applied at the audio sampling rate f_(s) suchas for example 48 KHz. The estimation of back-EMF parameters H₁(s) andH₂(s) at a lower sampling rate significantly reduces the processing loadof the illustrative system 400. In some implementations, N=8 and thelower sampling rate equals 6 KHz. The back-EMF to excursion mapping isexpressed as: In the Back-EMF domain:

${{{{\frac{{BEMF}(z)}{I(z)} = {{H(z)} = {{{H_{1}(z)}{H_{2}(z)}} = {H_{1}(s)}}}}}_{s = {2\;{fs}\frac{1 - z^{- 1}}{1 + z^{- 1}}}} \times {H_{2}(s)}}}_{s = {2\;{fs}\frac{1 - z^{- 1}}{1 + z^{- 1}}}}$$\mspace{20mu}{{H_{1}(z)} = \frac{b_{0}^{\prime}( {1 - z^{- 2}} )}{1 + {a_{1}^{\prime}z^{- 1}} + {a_{2}^{\prime}z^{- 2}}}}$For a speaker and passive radiator:

${H_{2}(z)} = \frac{( {1 + {a_{1}^{\prime}z^{- 1}} + {a_{2}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )}{\begin{matrix}{{( {1 + {a_{1}^{\prime}z^{- 1}} + {a_{2}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )} -} \\{b_{0}^{\prime} \times \frac{S_{d}^{2}}{2\;{fsBl}^{2}M_{ap}C_{ab}^{2}K_{S}}( {1 + z^{- 1}} )^{4}}\end{matrix}}$For a speaker and bass reflex port:

${H_{2}(z)} = \frac{( {1 + {a_{1}^{\prime}z^{- 1}} + {a_{2}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )}{\begin{matrix}{{( {1 + {a_{1}^{\prime}z^{- 1}} + {a_{2}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )} -} \\{{b_{0}^{\prime} \times \frac{S_{d}^{2}}{{Bl}^{2}R_{al}C_{ab}^{2}K_{S}}( {1 - z^{- 1}} )( {1 + z^{- 1}} )^{3}} -} \\{b_{0}^{\prime} \times \frac{S_{d}^{2}}{2\;{fsBl}^{2}M_{ap}C_{ab}^{2}K_{S}}( {1 + z^{- 1}} )^{4}}\end{matrix}}$In the excursion domain:

${{{{\frac{X(z)}{V(z)} = {{\overset{\_}{H}(z)} = {{{\overset{\_}{H_{1}}(z)}{\overset{\_}{H_{2}}(z)}} = {\overset{\_}{H_{1}}(s)}}}}}_{s = {2\;{fs}\frac{1 - z^{- 1}}{1 + z^{- 1}}}} \times {\overset{\_}{H_{2}}(s)}}}_{s = {2\;{fs}\frac{1 - z^{- 1}}{1 + z^{- 1}}}}$${\overset{\_}{H_{1}}(z)} = {\frac{1}{2f_{s}{BlR}_{E}} \times \frac{{{\overset{\_}{b_{0}}}^{\prime}( {1 + z^{- 1}} )}^{2}}{1 + {{\overset{\_}{a_{1}}}^{\prime}z^{- 1}} + {{\overset{\_}{a_{2}}}^{\prime}z^{- 2}}}}$where “s” is the continuous time variable and “z” is the discrete timevariable.The {b₀′,a₁′,a₂′} parameters are continuously adapted by minimizing theerror between the estimated back-EMF generated by the second orderfilter 422 and the measured speaker back-EMF provided by the back-EMFmeasurement 412 (as described herein).For a speaker and passive radiator:

${\overset{\_}{H_{2}}(z)} = \frac{( {1 + {{\overset{\_}{a_{1}}}^{\prime}z^{- 1}} + {{\overset{\_}{a_{2}}}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )}{\begin{matrix}{{( {1 + {{\overset{\_}{a_{1}}}^{\prime}z^{- 1}} + {{\overset{\_}{a_{2}}}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )} -} \\{{\overset{\_}{b_{0}}}^{\prime}\frac{S_{d}^{2}}{2{fsBl}^{2}M_{ap}C_{ab}^{2}K_{S}}( {1 + z^{- 1}} )^{4}}\end{matrix}}$$K_{s} = {{4f_{s}^{2}} + {2f_{s}\frac{R_{ap}}{M_{ap}}} + \frac{C_{ap} + C_{ab}}{M_{ap}C_{ap}C_{ab}}}$$s_{1} = \frac{{{- 8}f_{s}^{2}} + {2\frac{C_{ap} + C_{ab}}{M_{ap}C_{ap}C_{ab}}}}{{4f_{s}^{2}} + {2f_{s}\frac{R_{ap}}{M_{ap}}} + \frac{C_{ap} + C_{ab}}{M_{ap}C_{ap}C_{ab}}}$$s_{2} = \frac{{4f_{s}^{2}} - {2f_{s}\frac{R_{ap}}{M_{ap}}} + \frac{C_{ap} + C_{ab}}{M_{ap}C_{ap}C_{ab}}}{{4f_{s}^{2}} + {2f_{s}\frac{R_{ap}}{M_{ap}}} + \frac{C_{ap} + C_{ab}}{M_{ap}C_{ap}C_{ab}}}$For a speaker and bass reflex port:

${\overset{\_}{H_{2}}(z)} = \frac{( {1 + {{\overset{\_}{a_{1}}}^{\prime}z^{- 1}} + {{\overset{\_}{a_{2}}}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )}{\begin{matrix}{{( {1 + {{\overset{\_}{a_{1}}}^{\prime}z^{- 1}} + {{\overset{\_}{a_{2}}}^{\prime}z^{- 2}}} )( {1 + {s_{1}z^{- 1}} + {s_{2}z^{- 2}}} )} -} \\{{{\overset{\_}{b_{0}}}^{\prime}\frac{S_{d}^{2}}{{Bl}^{2}R_{al}C_{ab}^{2}K_{S}}( {1 - z^{- 1}} )( {1 + z^{- 1}} )^{3}} -} \\{{\overset{\_}{b_{0}}}^{\prime}\frac{S_{d}^{2}}{2{fsBl}^{2}M_{ap}C_{ab}^{2}K_{S}}( {1 + z^{- 1}} )^{4}}\end{matrix}}$$K_{s} = {{4f_{s}^{2}} + {2f_{s}\frac{1}{C_{ab}R_{al}}} + \frac{1}{M_{ap}C_{ab}}}$$s_{1} = \frac{{{- 8}f_{s}^{2}} + {2\frac{2}{M_{ap}C_{ab}}}}{{4f_{s}^{2}} + {2f_{s}\frac{1}{R_{al}C_{ab}}} + \frac{1}{M_{ap}C_{ab}}}$$s_{2} = \frac{{4f_{s}^{2}} - {2f_{s}\frac{1}{C_{ab}R_{al}}} + \frac{1}{M_{ap}C_{ab}}}{{4f_{s}^{2}} + {2f_{s}\frac{1}{C_{ab}R_{al}}} + \frac{1}{M_{ap}C_{ab}}}$

In the back-EMF to excursion mapping, the parameters {b₀ ′,a₁ ′,a₂ ′} ofH₁ (z) and H₂ (z) are derived from the parameters {b₀′,a₁′,a₂′} of H₁(z)and H₂(z).

${\overset{\_}{b_{0}}}^{\prime} = \frac{4b_{1}^{\prime}{KK}^{\prime}}{( {K + K^{\prime}} )^{2} + {( {K^{2} - K^{\prime 2}} )a_{1}^{\prime}} + {( {K - K^{\prime}} )^{2}a_{2}^{\prime}} + {( {1 - a_{1}^{\prime} + a_{2}^{\prime}} )\gamma\; K^{\prime}}}$${\overset{\_}{a_{1}}}^{\prime} = \frac{2( {( {K^{2} - K^{\prime 2}} ) + {( {K^{2} + K^{\prime 2}} )a_{1}^{\prime}} + {( {K^{2} - K^{\prime 2}} )a_{2}^{\prime}}} )}{( {K + K^{\prime}} )^{2} + {( {K^{2} - K^{\prime 2}} )a_{1}^{\prime}} + {( {K - K^{\prime}} )^{2}a_{2}^{\prime}} + {( {1 - a_{1}^{\prime} + a_{2}^{\prime}} )\gamma\; K^{\prime}}}$${\overset{\_}{a_{2}}}^{\prime} = \frac{( {K - K^{\prime}} )^{2} + {( {K^{2} - K^{\prime 2}} )a_{1}^{\prime}} + {( {K - K^{\prime}} )^{2}a_{2}^{\prime}} - {( {1 - a_{1}^{\prime} + a_{2}^{\prime}} )\gamma\; K^{\prime}}}{( {K + K^{\prime}} )^{2} + {( {K^{2} - K^{\prime 2}} )a_{1}^{\prime}} + {( {K - K^{\prime}} )^{2}a_{2}^{\prime}} + {( {1 - a_{1}^{\prime} + a_{2}^{\prime}} )\gamma\; K^{\prime}}}$$\mspace{20mu}{{K = \frac{2f_{s}}{N}},{K^{\prime} = {2f_{s}}},{\gamma = \frac{{Bl}^{2}}{M_{MS}R_{E}}}}$In these equations it is assumed that H₁(z) and H₂(z) are computed atlower sampling rate

$\frac{f_{s}}{N}$but the technique is equally applicable for implementations where H₁(z),H₂(z) and H₁ (z), H₂ (z) are computed at the same audio sampling ratef_(s), i.e., N=1.

The excursion protection 416 applies the excursion model received fromthe back-EMF model to excursion model conversion 420 in conjunction withan audio input signal to estimate speaker excursion resulting from theaudio input signal. The estimated speaker excursion is expressed as:Xest(t)= H ₁ (t)⊕ H ₂ (t)⊕In(t)where In(t) is the audio input signal.

If X_(est)(t) exceeds a predetermined excursion limit (Xmax), then theexcursion protection 416 limits the output signal amplitude as

${{Out}(t)} = {{{In}(t)} \times {\frac{X_{\max}}{X_{est}(t)}.}}$If X_(est)(t) does not exceed the predetermined excursion limit, theoutput signal is equal to the input signal (Out(t)=In(t)). The excursionprotection 416 includes a delay buffer 432 coupled to the audio input434 and the amplifier 404. The delay buffer 432 delays the audio inputsignal to allow a determination of excursion based on the audio inputsignal and attenuation of the audio signal before the audio signal isprovided to the amplifier 404. The delay buffer 432 provides 3-10milliseconds of delay in some implementations of the excursion controlcircuit 402.

A speaker system 406 with a bass reflex port is a fourth order system

$\frac{{BEMF}(s)}{I(s)} = {{H_{1}(s)}{{H_{2}(s)}.}}$However, if the port is closed (e.g., blocked by an object external tothe speaker system 406), then the system becomes second order

$\frac{{BEMF}(s)}{I(s)} = {{H_{1}(s)}.}$To accommodate variable port state, the excursion control circuit 402includes the port detection 418. The port detection 418 detects whetherthe port is open or closed. The port detection 418 is coupled to thevoltage sensor 410, the current sensor 408, and the second order filter422.

FIG. 5 shows an example block diagram for a port detection circuit 500in accordance with the present disclosure. The port detection circuit500 is an implementation of the port detection 418. In the portdetection circuit 500, BEMF(s) and I(s) are passed through an N-bandfilter bank 502 near the port frequency, and the magnitude of

$\frac{{BEMF}(s)}{I(s)}$is computed in each band. For each band, the computed magnitude of

$\frac{{BEMF}(s)}{I(s)}$is compared to a port closed reference 504 and a port open reference506. The comparisons produce a port open metric and a port closedmetric.

${{{{{Port}\;{Open}\;{Metric}} = {{\sum\limits_{i = 1}^{N}{\frac{{BEMF}(s)}{I(s)}}_{i}} - \frac{{BEMF}(s)}{I(s)}}}}_{{Port}\;{Open}}}^{2}$${{Port}\;{Closed}\;{Metric}} = {{{\sum\limits_{i = 1}^{N}{\frac{{BEMF}(s)}{I(s)}}_{i}} - \frac{{BEMF}(s)}{I(s)}}❘_{{Port}\;{Closed}}{❘❘^{2}}}$

The port detection circuit 500 deems the port open if thePortClosedMetric exceeds the PortOpenMetric, and closed if thePortOpenMetric exceeds the PortClosedMetric.

The excursion control circuit 402 applies output of the port detection418 to select second order or fourth order operation. The excursioncontrol circuit 402 includes a switch 426 that is controlled by outputof the port detection 418. The switch 426 is coupled to the currentsensor 408, the fourth order filter 424, the port detection 418, and thesecond order filter 422. If the port is closed, the switch 426 routescurrent measurements from the current sensor 408 to the second orderfilter 422. If the port is open, the switch 426 routes the filteredoutput obtained by passing the current measurements from the currentsensor 408 through the fourth order filter 424 to the second orderfilter 422.

Similarly, the excursion protection 416 includes a switch 428 that iscontrolled by the port detection 418. The switch 428 is coupled to theport detection 418, the back-EMF model to excursion model conversion420, and the audio input 434. If the port is open, the switch 428 routesexcursion estimates based on applying fourth order excursion model andsecond order excursion model to the audio input signal to the limiter430 for use in determining whether the excursion exceeds thepredetermined maximum. If the port is closed, the switch 428 routesexcursion estimates based on applying only second order excursion modelto the audio input signal to the limiter 430 for use in determiningwhether the excursion exceeds the predetermined maximum. The limiter 430controls the gain applied to audio signal received from the delay buffer432. The limiter 430 is coupled to the switch 428, the delay buffer 432,and the amplifier 404.

FIG. 6 shows an example of operation of the excursion control circuitexcursion control circuit 402. Signal 602 is an audio input signalreceived by the excursion control circuit 402. At time 604, theamplitude of the 602 increases to a level that would causeover-excursion of the speaker in the speaker system 406. The signal 606is the output of the excursion control circuit 402 (e.g., the signalprovided to the amplifier 404). At time 604, the excursion controlcircuit 402 detects the potential over-excursion and attenuates (appliesa gain attenuation to) the 602 to prevent damage to the speaker.

Some implementations of the excursion control circuit 402 omit the portdetection 418, the switch 426, and/or the switch 428 if the 406 includesa passive radiator rather than a bass reflex port. Some implementationsof the 402 include a digital signal processor (DSP) to provide thefunctions described herein. For example, a DSP executes instruction readfrom memory to provide the back-EMF measurement 412, the back-EMF model414, the back-EMF model to excursion model conversion 420, and/or theexcursion protection 416.

The above discussion is meant to be illustrative of the principles andvarious embodiments of the present invention. Numerous variations andmodifications will become apparent to those skilled in the art once theabove disclosure is fully appreciated. It is intended that the followingclaims be interpreted to embrace all such variations and modifications.

What is claimed is:
 1. An audio circuit, comprising: a speaker housing,comprising: a speaker; and a passive radiator or a bass reflex port; anamplifier coupled to the speaker; a voltage sensor coupled to thespeaker; a current sensor coupled to the speaker; an excursion controlcircuit coupled to the amplifier, the voltage sensor, and the currentsensor, the excursion control circuit comprising: back electro-magneticforce (EMF) measurement to measure back electro-magnetic force of thespeaker based on voltage measurements received from the voltage sensorand current measurements received from the current sensor; a back-EMFmodel that is updated based on measurements of the back-EMF and isconverted to an excursion model; and excursion protection to limitamplitude of audio signal provided to the amplifier based on theexcursion model of the speaker and amplitude of an audio input signal;wherein the back-EMF model comprises: a second order filter to modelback-EMF of the speaker; a fourth order filter to model back-EMF of thespeaker with the passive radiator or the port; further comprising portdetection to determine whether the bass reflex port is open based onvoltage measurements received from the voltage sensor and currentmeasurements received from the current sensor.
 2. The audio circuit ofclaim 1, wherein output of the fourth order filter is applied toestimate speaker excursion based on the bass reflex port being open, andoutput of the second order filter is applied to estimate speakerexcursion based on the bass reflex port being closed.
 3. An audiocircuit, comprising: an amplifier; a voltage sensor coupled to an outputof the amplifier; a current sensor coupled to the output of theamplifier; an excursion control circuit coupled to the amplifier, thevoltage sensor, and the current sensor, the excursion control circuitcomprising: back electro-magnetic force (EMF) measurement to measureback electro-magnetic force of a speaker based on voltage measurementsreceived from the voltage sensor and current measurements received fromthe current sensor; a back-EMF model that is updated based onmeasurements of the back-EMF and is converted to an excursion model; andexcursion protection to limit amplitude of audio signal provided to theamplifier based on the excursion model of the speaker and amplitude ofan audio input signal; wherein the speaker back-EMF model comprises: asecond order filter to model back-EMF of the speaker; a fourth orderfilter to model back-EMF of the speaker with a passive radiator or abass reflex port; further comprising port detection to determine whetherthe bass reflex port is open based on voltage measurements received fromthe voltage sensor and current measurements received from the currentsensor.
 4. The audio circuit of claim 3, wherein output of the fourthorder filter is applied to estimate speaker excursion based on the bassreflex port being open, and output of the second order filter is appliedto estimate speaker excursion based on the bass reflex port beingclosed.